Mathematical programming models for some smallest-world problems

Given a weighted graph G, in the minimum-cost-edge-selection problem (MCES), a minimum weighted set of edges is chosen subject to an upper bound on the diameter of graph G. Similarly, in the minimum-diameter-edge-selection problem (MDES), a set of edges is chosen to minimize the diameter subject to...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications Vol. 6; no. 5; pp. 955 - 961
Main Authors: Rosenberger, Jay M., Corley, H.W.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.12.2005
Subjects:
Binary programming
Minimum diameter graphs
Small world networks
Minimum diameter graphs
Binary programming
Small world networks
ISSN:1468-1218, 1878-5719
Online Access:Get full text
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Summary:Given a weighted graph G, in the minimum-cost-edge-selection problem (MCES), a minimum weighted set of edges is chosen subject to an upper bound on the diameter of graph G. Similarly, in the minimum-diameter-edge-selection problem (MDES), a set of edges is chosen to minimize the diameter subject to an upper bound on their total weight. These problems are shown to be equivalent and proven to be NP-complete. MCES is then formulated as a 0–1 integer programming problem. The problems MCES and MDES provide models for determining smallest-world networks and for measuring the “small-worldness” of graphs.
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ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2005.02.001